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All integers (whole numbers) can be expressed as fractions.

For example, the number 2 can be expressed as:


because 2 divided by 1 is 2.

Mixed fractions

When a fraction is combined with an integer, it’s called a mixed fraction.
Example of a mixed fraction:


From mixed fraction to fraction

A mixed fraction can be converted to a fraction if you multiply the integer by the denominator and add it to the numerator. While the result of this becomes the numerator of the new fraction, the denominator of the initial fraction of the mixed fraction is kept as denominator in the new fraction.

For example:


The numerator of the new fraction is 7, because the integer times the denominator plus the numerator is 7.

From fraction to mixed fraction

If you want to convert a fraction to a mixed fraction, you must determine how many times the denominator is contained in the numerator

In this fraction 3 is contained two times in the numerator 7 with the remainder of 1.
So the integer of the mixed fraction is 2 and the remainder 1 becomes the numerator of the fraction of the mixed fraction. The denominator of the fraction 3 is kept as denominator of the fraction of the mixed fraction.


If the numerator is divided evenly into the denominator, that is, there is no remainder, which is the case for the fraction frac{6}{3}, you won’t get a mixed fraction as result, only an integer: